For which equation is the order of steps to first divide both sides by 2 and then to subtract 10 from both sides?(1 point)

Question

Responses

2(x − 10) = 16
2 Left Parenthesis x minus 10 Right Parenthesis equals 16

2x + 10 = 16
2 x plus 10 equals 16

10(x + 2) = 16
10 Left Parenthesis x plus 2 Right Parenthesis equals 16

2(x + 10) = 16

Answer 1

The equation for which the order of steps to first divide both sides by 2 and then to subtract 10 from both sides is 2(x + 10) = 16.

Here's the reasoning:

1. Start with the equation: \(2(x + 10) = 16\)
2. Divide both sides by 2: \((x + 10) = 8\)
3. Then subtract 10 from both sides: \(x = 8 - 10\) which simplifies to \(x = -2\)

If you apply the same steps to the other equations:

1. For 2(x - 10) = 16:

   • Divide by 2: \(x - 10 = 8\)
   • Subtract 10: \(x = 18\) (not applicable)

2. For 2x + 10 = 16:

   • Divide by 2: Not correct, can't start by dividing both sides directly by 2.

3. For 10(x + 2) = 16:

   • Divide by 10: \(x + 2 = 1.6\)
   • Subtract 2: \(x = -0.4\) (not applicable)

Thus, only 2(x + 10) = 16 fits the order where we correctly divide by 2 first and then subtract 10.